The bailout, the largest in United States banking history, has two basic thrusts: to shore up the bank's financial condition with $4.5 billion in assistance; and to beef up management by installing new top executives. The goal is to produce a smaller bank able to stand on its own and less dependent on volatile sources of funds.

The rescue operation was masterminded by the Federal Deposit Insurance Corporation (FDIC), the Comptroller of the Currency, and the Federal Reserve Board.

In July 1982, Continental Illinois announced that it would suffer large losses because it had purchased $1 billion in energy loans, many of poor quality , from the failed Penn Square Bank of Oklahoma. Since May 1984, Continental has been kept afloat by a $7.5 billion temporary aid package assembled by the FDIC and 28 major banks.

By purchasing many of the bank's bad loans and injecting new funds, the regulators ''have created through this transaction one of the very strongest banks in the world,'' said FDIC chairman William M. Isaac. The bank's ratio of capital (or owners' equity) to assets (or loans) will be about 7 percent, he said, putting it among the highest in the industry.

As part of the package the boards of directors of the bank and its parent company have named two new chief executive officers. Each will be paid $600,000 and granted options to buy stock. John E. Swearingen, former chief executive officer of Standard Oil Company (Indiana) has been named board chairman and chief executive officer of Continental Illinois Corporation, the bank's parent. William S. Ogden, former vice-chairman of Chase Manhattan Bank, was named board chairman and chief executive officer of Continental Illinois National Bank.

''We have found two of the world's most outstanding executives to come in and take control,'' Isaac said. ''The FDIC will not be running the bank.''

The bank's two current top officers have resigned their positions and board seats effective Aug. 13, but they will serve as vice-chairmen of the bank until a new management team is in place.

Before the aid package can take effect, Continental's existing shareholders must approve the transaction, which gives the government 80 percent of the bank's stock, thus severely reducing current shareholders' ownership position. Approval is expected within 45 to 60 days, Isaac said.

The bailout is controversial.

Treasury Secretary Donald T. Regan says the bailout is ''bad public policy'' because of the protection it indirectly offers holders of Continental bonds. Issac said protection for the holding company bondholders was ''troubling'' but that due to technical factors no workable way around the problem was found.

House Banking Committee chairman Fernand J. St Germain (D) of Rhode Island said the bailout ''raises the greatest array of questions in the history of the federal bank regulatory system.'' He complained that the deal was completed without public debate, created large contingent liabilities for the federal Treasury, and reshaped the banking industry without review or prior approval. FDIC chairman Isaac said the government ''is not going to lose a significant amount of money'' on the package.

Under the terms of the bailout, the FDIC will:

* Spend $2 billion to buy troubled loans Continental now values at $3 billion. The resulting $1 billion write-down in stockholder equity is the largest in US banking history.

* Buy an additional $1.5 billion in bad loans for full value over the next three years. But Continental will not be able to sell the government bad loans made to foreign governments.

* Buy $1 billion in nonvoting preferred stock. The shares can be converted into 80 percent of Continential Illinois Corporation's common stock. If the FDIC loses money on the rescue plan, it may acquire at bargain prices the remaining 20 percent of the stock.